Killing spinors from classical r-matrices

Orlando, Domenico; Reffert, Susanne; Sekiguchi, Yuta; Yoshida, Kentaroh (2018). Killing spinors from classical r-matrices. Journal of physics. A - mathematical and theoretical, 51(39), p. 395401. Institute of Physics Publishing IOP 10.1088/1751-8121/aad8c2

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The Yang–Baxter deformation (yb deformation) is a systematic way of performing integrable deformations of 2D symmetric non-linear sigma models. The deformations can be labeled by classical r-matrices satisfying the classical yb equation. This yb deformation is also applicable to type IIB superstring theory defined on AdS. In this case, a simple class of yb deformations is associated with TsT transformations of string backgrounds. The data of this transformation is encoded in an antisymmetric bi-vector Θ (which is often called β field or non-commutativity parameter). In this article, we give a simple recipe for obtaining the explicit expression for the Killing spinors of the TsT transformed background starting from Θ. We moreover discuss the M-theory equivalent of the TsT transformation, allowing us to also give Killing spinors of 11D backgrounds. We discuss examples of TsT transformed backgrounds starting from flat space, and . We find that in this way we can relate the Ω-deformation to yb deformations.

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